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Objectives Solve quadratic equations by completing the square.

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Presentation on theme: "Objectives Solve quadratic equations by completing the square."— Presentation transcript:

1 Objectives Solve quadratic equations by completing the square.
Write quadratic equations in vertex form.

2 Vocabulary completing the square

3 Read as “plus or minus square root of a.”
Reading Math

4 Example 1: Solving Equations by Using the Square Root Property
Solve the equation. x2 = 121

5 Example 1: Solving Equations by Using the Square Root Property
Solve the equation. x2 = 121 Is this the same as “What is the √(121)?”

6 Example 2: Solving Equations by Using the Square Root Property
Solve the equation. x2 = 1296

7 Example 3: Solving Equations by Using the Square Root Property
Solve the equation. 4x = 59

8 Example 4 Solve the equation. 4x2 – 20 = 5

9 If a quadratic expression of the form x2 + bx cannot model a square, you can add a term to form a perfect square trinomial. This is called completing the square.

10 Example 5: Completing the Square
Complete the square for the expression. Write the resulting expression as a binomial squared. x2 – 14x +

11 Example 6: Completing the Square
Complete the square for the expression. Write the resulting expression as a binomial squared. x2 + 9x +

12 Example 7 Complete the square for the expression. Write the resulting expression as a binomial squared. x2 + 4x +

13 Example 8 Complete the square for the expression. Write the resulting expression as a binomial squared. x2 – 4x +

14 Example 9 Complete the square for the expression. Write the resulting expression as a binomial squared. x2 + 3x +

15 You can complete the square to solve quadratic equations.

16 Example 11: Solving Equations
Solve the equation. x2 + 12x + 6 = 0

17 Example 12 Solve the equation. x2 + 8x - 33 = 0

18 Example 13: Solving a Quadratic Equation by Completing the Square
Solve the equation by completing the square. x2 = 12x – 20

19 Example 14: Solving a Quadratic Equation by Completing the Square
Solve the equation by completing the square. 18x + 3x2 = 45

20 Example 15 Solve the equation by completing the square. x2 – 2 = 9x

21 Example 16 Solve the equation by completing the square. 3x2 – 24x = 27


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